{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pwlf\n",
    "# generate sin wave data\n",
    "x = np.linspace(0, 10, num=100)\n",
    "y = np.sin(x * np.pi / 2)\n",
    "# add noise to the data\n",
    "y = np.random.normal(0, 0.05, 100) + y\n",
    "my_pwlf_2 = pwlf.PiecewiseLinFit(x, y, degree=2)\n",
    "res2 = my_pwlf_2.fitfast(5, pop=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "# first line\n",
    "xhat = np.linspace(my_pwlf_2.fit_breaks[0], my_pwlf_2.fit_breaks[1], 100)\n",
    "yhat = my_pwlf_2.beta[0] + my_pwlf_2.beta[1]*(xhat-my_pwlf_2.fit_breaks[0]) + my_pwlf_2.beta[6]*(xhat-my_pwlf_2.fit_breaks[0])**2\n",
    "plt.figure()\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xhat, yhat, '-.', label='First segment')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# second segment\n",
    "xhat2 = np.linspace(my_pwlf_2.fit_breaks[1], my_pwlf_2.fit_breaks[2], 100)\n",
    "yhat2 = (my_pwlf_2.beta[0] +\n",
    "         (my_pwlf_2.beta[1])*(xhat2-my_pwlf_2.fit_breaks[0]) +\n",
    "         (my_pwlf_2.beta[2])*(xhat2-my_pwlf_2.fit_breaks[1]) +\n",
    "         (my_pwlf_2.beta[6])*(xhat2-my_pwlf_2.fit_breaks[0])**2 +\n",
    "         (my_pwlf_2.beta[7])*(xhat2-my_pwlf_2.fit_breaks[1])**2)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xhat, yhat, '-.', label='First segment')\n",
    "plt.plot(xhat2, yhat2, '-.', label='Second segment')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Third segment\n",
    "xhat3 = np.linspace(my_pwlf_2.fit_breaks[2], my_pwlf_2.fit_breaks[3], 100)\n",
    "yhat3 = (my_pwlf_2.beta[0] +\n",
    "         (my_pwlf_2.beta[1])*(xhat3-my_pwlf_2.fit_breaks[0]) +\n",
    "         (my_pwlf_2.beta[2])*(xhat3-my_pwlf_2.fit_breaks[1]) +\n",
    "         (my_pwlf_2.beta[3])*(xhat3-my_pwlf_2.fit_breaks[2]) +\n",
    "         (my_pwlf_2.beta[6])*(xhat3-my_pwlf_2.fit_breaks[0])**2 +\n",
    "         (my_pwlf_2.beta[7])*(xhat3-my_pwlf_2.fit_breaks[1])**2 +\n",
    "         (my_pwlf_2.beta[8])*(xhat3-my_pwlf_2.fit_breaks[2])**2)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xhat, yhat, '-.', label='First segment')\n",
    "plt.plot(xhat2, yhat2, '-.', label='Second segment')\n",
    "plt.plot(xhat3, yhat3, '-.', label='Third segment')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fourth segment\n",
    "xhat4 = np.linspace(my_pwlf_2.fit_breaks[3], my_pwlf_2.fit_breaks[4], 100)\n",
    "yhat4 = (my_pwlf_2.beta[0] +\n",
    "         (my_pwlf_2.beta[1])*(xhat4-my_pwlf_2.fit_breaks[0]) +\n",
    "         (my_pwlf_2.beta[2])*(xhat4-my_pwlf_2.fit_breaks[1]) +\n",
    "         (my_pwlf_2.beta[3])*(xhat4-my_pwlf_2.fit_breaks[2]) +\n",
    "         (my_pwlf_2.beta[4])*(xhat4-my_pwlf_2.fit_breaks[3]) +\n",
    "         (my_pwlf_2.beta[6])*(xhat4-my_pwlf_2.fit_breaks[0])**2 +\n",
    "         (my_pwlf_2.beta[7])*(xhat4-my_pwlf_2.fit_breaks[1])**2 +\n",
    "         (my_pwlf_2.beta[8])*(xhat4-my_pwlf_2.fit_breaks[2])**2 +\n",
    "         (my_pwlf_2.beta[9])*(xhat4-my_pwlf_2.fit_breaks[3])**2)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xhat, yhat, '-.', label='First')\n",
    "plt.plot(xhat2, yhat2, '-.', label='Second')\n",
    "plt.plot(xhat3, yhat3, '-.', label='Third')\n",
    "plt.plot(xhat4, yhat4, '-.', label='Fourth')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Zb8KglETAGD75Qq5/egFCF9jpMSYhkbtefI2ss8cFdNzTQSmKHpJfYOb7L95Cj5PPHRMDH+tubYQV/w17lwVmvF7MqOIfqIqMY2dytle7L6OQTtQLs3jlTnz91qeY/+s3QRs+GS40NzTgsNs0lcHpdGC3aStDe5Si6CELlxZysfyeA85+7JGusLaAxrobomDTm1DwTmDG66U4LRbOObaHtWmjcQrvx8aXUUidncVtsTn45rud1H3+Oc07fFd3SNGR9R+/y6v33oHT4Th1Zz9QX1XBX++5lV2rV2gyflcoRdFD6msqmKTbxVLnubhLdkAAY911esi9Aoq/BltzYMbshTSsWUOkw8YPA/O82n0dhdTV9+arPjlgMFD/9dc+G0vhwtPV939FEZgmXIpOrz/1C/0gx2WvbKWiycGb738ZVBn4SlH0kKvjdhEhHHztGO/VHtBY9+GzwNoAB78L3Ji9jIZly9HFx3Pz3Ve1FXTzR8hkV9+bPn2TiTn3HOqXB9dKM9Rp7+rb4kjlD0f6BnySbpOjtplDpoGk1h3i0Y+3BI2yUIqih0yfeA7vOS+hQJ7I4Ax4rHv2VDDGwp7PAzdmL0La7TSsWkXctAuZM2Egax+5iAMLZvrloJn2ZajhxPcp9qKLse7fryrK+hBPV19qSzmpLeVYrPaAl0nxlONQdCZGaSO+4WjQlGtRiqKHXHjxTKLm/h9pCTEBScxpT36BmcnPr+NLywiObfqM/M0lARm3tzFgwe9JvOVWv4/Tvgy15/cpbvo0ABpWrvK7HL0FT1ffuTUbueL40g7tgZbjSFQGTgQDLUeCplyLyqPoCTWHwWZhTt4wTZKgThzU7mCFfiyX63/grU+WgLhSJWX5EGEwEDc9cLkq7ctQu/n8OMQkprHt9Y948fgglXznA9ISTJhrLAjpJN1SSnHsEBAi4GVS3HIAWPWRHIvsS6alhJLsCwMqR1coi6Kb5BeYeefPT2B9aRKXLPhCE1+ip7m6yuHaZJ3k3BQ05mq4UPWvd2jZt09TGdyLgrUpwzmr6iDV5VWq5LgPcLv6+rYcJ1JaORKVgcAVluyrw4rORA43R0wZ9Gs5TnllTUDl6AqlKLqB+6F9qfFi7rU9SHEtmjy0nmZpOQnscGYxTb81aMzVcMBeXk7Zs8+y4KnX2xLgtFwU/NB/BHrpZNzxIlVy3Ae4XX1ncRwAsykdd6ZKIHOiPF2OACVRGeiQpDeXBsU5JEpRdAP3Q3uUZJY5XdFOWjy07c3jTxyT2etMJy1elR33FUtKrNxx5TN82HespocHuZX/7sSBfJc2hnpjtFe7ovvMGZvOZUn11JhSsei9n6lAPtfuw8nSE0wcjeqHTRjIaDYHXI7OUIqiG5TWWJik28kN+hUYsHu1B5L25urrjpn8P/Ez5l02PKByhDMLlxZyTGeiwXiirLiWiwKnTs//nHsbW1NzvNoV3cdutVJatJuDEQM6va7FxrZT6FmRciG74kZ4tWuFUhTdIC3BxI36FTxk+Ag7eq/2QNJphMzcUczJUbWffIG027lz6V8Ze7xj6XitFwWJzXWkymZVctwHHN1biMNmoyklu9PrWmxsAxTFDqPSmKyZHJ4oRdEN5l2awxTdDtY4R+HOxtbqnAC3uXpgwUzmzcglcsl9HPjj5KDYAAt1mnfs4PyjO4jp5LwPLRcFKZZa/v3VMzzXx6yinnzAkZ3bQQhumj2tyxyWQOJeFOikg8GNB0hpqdD8HBIVHtsN5gyoBlHPrqixCJtr0tA6VNG9wX6u4zz6ixxKaxr9XgI73GlYtw4pBIUDvB9QLRcF7s+y6t8weOKkgMsQjhzbX0zfQYO5ZlIO+qhoFi4tpLTGotlz7R7vuS93cemhZRxKGc2Mq3+k6XMswq0a5YQJE+TGjRv9O8i6P8PXj8NDu6FPmn/HOk0mL1jRFoftSXqCibWPXKSBRKHPoVtvw9nYyNYnXtR88mhPfoE56GQKVZxOB021tcQmJmktSgfKDx8kcUA6hogIv48lhNgkpZzQ2TVlUXSHA6sheWjQKAnw9plniONkiAr+4xypomK6idNiwbJlC4m33dplApxW5BeYeerDTZxVsgtn/ADMpCjrsQfodPqgVBJA0BxgpOkehRDiMiFEoRBirxDikU6u3y6EKBdCbGn9+akWcnrhsMOh9a76SkGEp8/8t4b3+N+IvwBSRcV0k6bNm5E2GzETJ2otSgcWLi1EWpp5YsNbTC3ZCmgfPhmq7Px2Ocv+/hfNyoqfiqa6Wr791z8oLdqtqRyaKQohhB54GbgcGAncKIQY2UnX96WUea0/fw+okJ1xdCtY6yFritaSeOEZFfMf50gGiCqGR5SrqJhu0rThB9DriR4XfKeNldZYqIuMYX+fAYyp2OvVrjgzao+XUbavWJOy4qdDhDGSjUvyeeqlDzVN+NTSojgX2Cul3C+ltALvAVdpKM8pyS8w8/KbbwJw5WKCKqrIMyrmP05X7PXvx9cpV0Q3adqwgahRZ6GLidFalA64rcRtKUMYWXUQg9Pu1a44fc7/8c3c/D9/0lqMLvl8dyXlxhRia0s0TfjUUlGkA0c8fi9pbWvPNUKIbUKIj4QQmYERrSPuqCJdczW7nIPYXhuleVp9e9yhssv/526I6ctY506tRQpJnBYLlu3biTn3XK1F6RS39bg9ZQhRDhs51SWah0+GMkKIU3fSiIVLCzFH9qNfy3F00uUe08LNqKWi6OzTaR+CtRjIklKOAZYBb3V6IyHuEUJsFEJsLC8v97GYLtxlO/5gv5GZ1meBIPYLC4E5fixl25Zraq6GKo7aWmKnXUjM5Mlai9IpbuuxcrDLUzu58XBAS9uHC7tWr+Dteb+ksaZaa1G6pLTGwtHI/kRIOynWSq/2QKKloigBPC2EDKDUs4OUslJK2dL662uA9zFyJ/q9KqWcIKWckJqa6hdhPT8Y6fG2BaNfOL/AzBslA+hPBWmUB0VRsVAion9/Ml96KSg3st3MGZvO0qdnYxw6hNtiq5WS6AbmPbuoqywnuk+81qJ0SVqCibKofgD0bznm1R5ItFQUPwA5QohsIYQRuAH4zLODEMKz+MpsQLOtf1fZjuUsMj5JDBav9mBj4dJC1tmGAXCOzmXxBK31E4Q46uu1FuG0iR4/AcumzcggjdoJZkqL9zBgaC5CF7wFKubNyMURFU+DPob+zS5FoYWbUbN3SEppB34JLMWlAD6QUu4UQjwjhJjd2u0BIcROIcRW4AHgdm2kdX1gVn0M5TKBRlzKIVj9wqU1FvbIgdRJU5uicLcrTo602SieeiHfPb6AyQtWBL3rLnrCeJyNjbQUdaxHpegaq6WJyiOHGZATfM+vJ3PGpvP7a8ZQG5dG/5ZjAT9B042mCXdSyi+AL9q1Penx//nA/EDL1RmuD+bnPLN0OiLIs2Hdp2UVOHMYq9vr1a44OdJm49jcW3jhaBRmu0uxul13EHwJbe7w3ebCQqJGjDhFb4Wbsn17kdLJgJzgr7Q8Z2w66TOnsPqdN/jm3vGauMpUZvbpYmtmzqhk5owN/nIY82bkMn/Rdh6x3U01sUDwWj/Bhi46mkeNeZjjva0vt+su2BSFIS2NnPXrMCQmai1KSHF0r8vS7j90mMaSnB4DcnJJHJBOQ1WlUhRBzZ4l8MnP4RfrIDW4v1zuyWzh0kJaaiykB7H1E0zkF5j58J2vaXCYIDKuw/VgdN0JIZSS6AZlewtJHJCGKbbj5xyMZIwYxZ0vvKLZ+MG7ixNsHNkA+ghIGqy1JKfFnLHprP3tdA5cWsDay8qUkjgF+QVm5n+8jZ8v+xs/2/5Zp32C1XVn2b6DI/feh+3YsVN3VgBQtreI/kOCe8EXTChFcbqUbID08aAPISNMCNi7HMybtJYk6Fm4tJC4ugpSmuvYlZTV4Xqwu+6sBw5gP35cazFCgoaqShqqq+g/JEdrUc6IzV9+xhu//jlaVPwOoVlPQ2wWKNsO5z+gtSRnzk+XQxCH/wULpTUWplYdAmBP0iCva8HuujONHsWQL784dUcFAFJK+oybxmPfN7Nn9edBHZjiSVxSCgNyhmNvaSEiKiqgYytFcTqUbgGnHTLO0VqSM0cpidMiLcHE8G2HadZHcKDPifQddZ5H+LH8cAt/ahiFxebKPQnmqDZPcs47n5zzztdkbDWLnA7m1oOQQlFRNFXBGzNh2wdaSxLUzJuRy8iawxQnZODQuSqJBru7yZOajz6ieNp0pNWqtShBz8ufbaDZavNqC5WEVCklLU2NAR9XKYrToWQjJAyEWP+UB/ErUQlwbDscWqu1JEHN7LNSGVpXirn/YARoltjUHfILzDy57CD2sjJuefSdoE0ODAaklEzd8w7TK1Z3uBaMUW3t+ei/H+PT554N+LjK9XQ6mDdBRqcnBAY/Op1rE75EbWifjJY9e9DZbdx195X8+rIZWotz2rirGscYB/ALIOlwEfMXuVxnoaDkAo2UTnZkTuewNbLDtWCNavMkcUA6e9auRkoZ0Kq3yqI4FQ3HofaIa7INVdLHw/FdYG3SWpKgxbLN5aM2jRmtsSRnhruqcYUpnqrIOIZVHwkZN4oW6HR6brxxDjVxGV7toeJm7Js9lJamRmqOHQ3ouEpRnApDJMz+Mwy7XGtJuk/aOJAOKNumtSRBS/P2behTUzAMGHDqzkFEm7tECAoTBzKs+oh3u8KLsn3FTIq3tB3yFWpuxn6DhwJw/MD+gI6rXE+nIioext2mtRQ9I731OE/zZhgYvKWztaTvww+TaDYH9SE2neGu6wVQlJjJpLKdRNssJKYmaSxZcLL+o39TV36cnzz3ckgohvakZA5Epzdw/MBecicF7jhmZVGcin0roXKf1lL0jLj+0CddJd6dBENyMqYxY7QW44zxPCu9KMF1vMtZDUdDwo2iBccO7KNvVmhUV+gMvSGClMxBHDsQ2DlJWRQnQ0qaP7iL5faz+WXjT0MmMadT0sbC0S1aSxGUNBcV0bh6NfHXXBNydZM863rttbr87ven2Zgait9RP9NYU01jdRV9s4doLUqP6Js9mH2bNgR0Q1tZFCchv8DMtU2P8nzTFZoebO4T0vKgci8012otSdBh2bSJ4889DxqURvAF7rPSt/3pOiIyMhhcdVhrkYKS4wddfv1QtigAUgcNxlJXS0N15ak7+wilKE7Cwq+L2GEbwH6Z1tYWshElWRfAmOvBGvhknWAn8cYbGfaf9RiSQt+vn3jTTcRMmqS1GEGJW1GkDgptRdE32yV/IDe0levpJIysW8MkfQMfOS70ag/JiJKBE9VG9knQJyRoLYJPSL7zDq1FCFrKD+6nT2o/omJjtRal2+QXmPnfL46QnDSJpUtKuFeXHhBXuFIUJ+HOqBUk2Cs6KIpQSMzpFCmhuQZMoeWH9yefrS2k/ndP8e9BU6gZMjJ096A8sFdXI4QIG+XnK/YXFXPIHkv2I6FTCNATd3KlxebgUHweWAhYjSrleuoKKRkbcZg9eJupoZKY40l+gZnJC1bwyZOzOPzH80Nzj8UP5BeY+efbXzPu8Fai7C2hvQfViqOujuJJ51P94YdaixJULNpwgJbKYxwRiSG73+hOrgQwOZpIt5gD5gpXiqIr6suIaqlkyNmTQzIxx417FWKusbDEcR6vWmcwf9G2kHpA/MXCpYVkVrg2fvcmuD7TkN2DakXfpw/9n3qS2KkXnrpzL+Ifi9ejQ1JhTG5rC7XP2tPlPapuF3PLPiPCaQuIK1y5njohv8DM2i/+xULgr4UxzLs8tExUTzxXIcudrWVIHM6gPP850JTWWBhSW0q5KZ5aj6NPQ3IPqpX8AjMLD/WjdGsxaQklIede8Re7rbGUpf2YOoP30aeh9Fl7JlcWxg7DbErDIXQBcYUri6Id7hV4/6YinFKwuq5/yJmonng/CJJBooyB4lhIPSD+Ii3BxNDaEvbFp3doD0Xc393a45WcU7aLioqakP7u+pL+ibFURKZg1XsXAwylz9ozubIuog+lUWlEGo0BcYUrRdEO9wp8pO4QB2U/GjGFnInqSfsH4WPj09yr/zSkHhBf496zqaioJb2+3EtRhOIelJu2727VQX73n38wtCZwPuxg556UUnJajni1hdpnPWdsuhsB5YQAACAASURBVFeNqvHiKI+PCUyVYKUo2uFeaZ8lDrJLZnVoDzU8VyEg2OUcxGj9oZB6QHyJ555NVt1R9Ej2tyqKUNyD8sT9HXUrviG1Zq/23kzzpm+4rm9dSO83wonkygMLZnJRy3Z2fPkJ2Y98zuQFK/xqOao9inakJZioq6lkoK6c92wXebWHIp4lHkprLBw2DmWyXMJZY/pqLJk2eO7ZuCfSvQlpYXHkqduHXRnVhxpjDENqS9vaezt3v/wP7C0t3G2K1loUn5BfYKagIYpsyxGklH4/zlVZFO2YNyOX3Ijj2KSeXXIQEHomans8VyG3XDUTvdMGFUVai6UJnqvrwbWl1EeYOG5KDItVd5v1KAT749MZXFsa8t9dX6HT6TGGiZIA14LnmCGJKKeVGIer2oI/3YxKUbRjzth0brl6Dj+Kepd1zlEha6J2Sf/Wg3nKdmgrh0Z4rq5b9EYKUnNAiLBYdXv6sPfHpzGo/hi/nz0ifL673WTP2m/55rWXcDocWoviM0prLFQaXSVnUqyVXu3+QLmeOmHO2MCkxWtC8lDQR7oOMTr7eq2lCTjzZuS2Zbe+Nno2EPoWoyfu727t4iZK563isj4tWoukOQcKNnJ4x1YuufuXWoviM9ISTFRUuhRFkrWKQ9GD2tr9gbIoOmPJr+GHv2sthX/QG6DvCDi2U2tJNKF95EjYWYytROYOA6ClcI/GkmhLfoGZdRt3sqs5xu8bvoFk3oxcdFExNOhjSLZVAf5d8ChF0R4poaIY6su0lsR/9B/VaxUFuJTFl+MdLNv6MitvGRZ2SgIgMjsbERFB857eGxqbX2Dm0Y+3EttcSUVEUkiW7egK94KnMTqFZGuV3xc8SlG0Rwi4fQlc9LjWkviF/AIzL2w3QuNxZv1+UVg8NN1BH9eHyKFDMKSmai2KXxARERhzhtKyp/daFAuXFhJhqcYgHW3+/HDKK5kzNp0rpo4lTdbx3cMX+nXBo/YoehHuHIJEWx7f6x6juFkErPpksBEz8TxiJp6ntRh+Zc/tD/HSxnJ2h2i11J5SWmMh2+pyy1QZk7zaw4XkzIHYbVbqjh8nof8Av42jLIr2fPc8vH4pOJ1aS+Jz3DkEpaSw3nkWLRjDaoV1JjgaGrQWwa/kF5j5rx8a2GU1hmy11J6SlmAiyVoNQHVEold7uJA7cQr3vv6uX5UEKEXRkZJNYKkBXfi9NZ4rqSm67Vyi29ihvTfgaGigaMI5VL31ltai+I2FSwsxNNZxbfFKBtUdBcLL7XI6zJuRS19HNbWGOGy6CCC8ItwAjKZoTLFxp+7YQ8JvNuwm7vo/h3dvYHlVSliuvDxXUvfol/CAYVGH9t5AS1ExABGZAzWWxH+U1ljQO53ctfNzRlYe9GrvLcwZm86IqCaaolPCOsJt85eL2fzlYr+OofYoOOG7F7ZGBkaV80HLNF4PQ9+9Zw7Bw7Z7qCMGgcstMXnBil7jw24pdimKyGHDNJbEf7jKecC1V/w/Go0mr/begsPuoI/JxFWTx/HcjTO1FsdvHNq2GYRg3OVX+m0MpSg44bvPEyUAFMrMNjM9nCZOz7pP5ppkBCBbr/m7Vkww0VJUhC46moj0NK1F8RvuRUEjJxRDuLldTkVzo52I2BvpO3iQ1qL4lTnznkD42VWuXE+cMMeH6VxliAtlpld7OOGu+zQ83sE8w3uMFyd81r3Fh91SXExkTg5CCK1F8RvuOPsZDfuZ/8M/yYiPDEu3y8mIiY/kpqfOI/e8/lqL4lf8rSTgNBSFEOKXQojEU/ULZdzmeK4ooUlGckSmerWHI4dq7fxcv5gpOu+aT+GoHD2RUtJSVETksBytRfE7c8ams2BqP6aat7Lilt7hVuyN1FUcZ9Hvn+Lwjq1+G+N0VFF/4AchxAdCiMuED5dhrfcrFELsFUI80sn1SCHE+63XvxdCZPlqbE/cVTeHiSMUy3QkurA305MSEjgk+5KjK/FqD2flCOCoqMBRU0NkTvjuT3gSmeNSiO59md7E6veKWPbGLq3F8DtGUzQHtmyibJ//PuNTKgop5eNADvA6cDtQLIT4HyHEkJ4MLITQAy8DlwMjgRuFECPbdbsLqJZSDgX+F/hDT8bsCreZPkJvpsiZEbbREZ7Mm5HLPpHJMHFCUYS7cgRo2bsXoFdYFOChKIp6n6IoLa6mucmmtRh+JyomlpjEJKrMR07duZuclnNLSimBstYfO5AIfCSE+GMPxj4X2Cul3C+ltALvAVe163MV4A52/wi42JcWjSdzxvQjJW8mP77uNtY+clFYKwlwKcfM3PFk6o4RgbVXKEfwiHgaOlRjSQKDPjaWkrteZnf0RK1FCSgOh5PqY00kp8VoLUpASE7PoMpccuqO3eSUUU9CiAeAnwAVwN+BeVJKmxBCBxQDD3dz7HTAUwWWAO1rKrT1kVLahRC1QHKrLJ4y3gPcAzBwYDdj4/UGmPNy914bohyfeBE3O1fwxcxR5CT2jhX2uuQqom6cyvDkZK1FCRgtpmQqD/WucuO1xy047ZKkAb1DUSSmZbL7u5VIKf0SpHE6FkUKcLWUcoaU8kMppQ1ASukEZvVg7M7+GtmNPkgpX5VSTpBSTkgN0yJv/qBvQjYtjhb21uzVWpSA8Z7YyDvnWcM64qk9SWkxVB9rxOEIv7I0nZFfYObev3wPwH8t3R2WybPtMcs4rJYmRs/70C/l1E9nj+JJKeWhLq7t7sHYJUCmx+8ZQGlXfYQQBiAeqOrBmAoPsuOz0Qs9xdW9w38tpWRfzT6GJvQOt5Ob5LQYnHZJ7fHwjmiDE8mz+jobTiR7msK/xlV+gZm3d7s+23hbjV/qemmZR/EDkCOEyBZCGIEbgM/a9fkMl9sL4FpgRet+icIHGPVGBvYZ2GssimNNx2iwNfQ6RZGUFgtAVWmjxpL4H3fybIpTR41OYhfhnx+0cGkhZaIPAIk2VxFEX//NmikKKaUd+CWwFNgNfCCl3CmEeEYIMbu12+tAshBiL/AQ0CGEVtEzhiYM7TWKoqi6CIAhCT0K2As5EgdEIwRUmsO7Yi6cyANKcQjK9bJDezhSWmOhUR+DVUSQaKvxavcVmpbwkFJ+AXzRru1Jj/83Az8OtFy9iZyEHJYdWkaTrYnoiGitxfErqaZUrs+9vtds3LsxROiJ7xvdKxRFWoKJY9UWEp2C3REOr/ZwxVXXy8IhUyZWndGr3VeoEh69nJzEHCSS/bX7tRbF74xIHsHjEx8nPjJea1ECTnJ6TK9QFPNm5BJv0FMY4cBscG3eh3t+kDth+Kt+M/g+8VzA93+zKgrYy3H764urixmVMkpjafxHfoGZPyxbR1llJGkJsb2mUq6b4zon9RXNDPvt56Qmhu9pd56FL0trbKT3gpP9vP9mi19OM1SKopeTGZdJlD6qzX8fjrgiYbagH/wsEbopmMsv7zWVcsH19/+ruIwxBh2RUoR9peBZo/qH5d91MuaMTffr36xcT70cvU7P3WPu5pz+52gtit9YuLQQi91Oc9nV2OtHA+EfCePJwqWFFAk7H8Vaqde5NnjD+e9f8tI2Fv/ZfwXyeiPKolBwz5h7tBbBr7iiPwzYa8d30h7+eP2dkrY01nD9+3Mm9EWn7z0JlYFAWRQKnNLJ4brDWOzhOXGkJZjQRZnRRZZ2aO8NuP/OmY0RXN/on6iYYOKsC9IZcX74HkqlBUpRKNhYtpGZn8yk4HiB1qL4hXkzcjH1XUZU2vttbeEeCeOJOyrmiMHJ/jCPBGqqs1Jf1YzKy/UtSlEoGJE8gmfOfyZsM5bnjE0nMaGCSJmBgF5TKdeNu4x+ZT8jG6PsYf33715XytuPrsNqsWstSlih9igUxBnjmJszV2sx/EZtSy21tnIenHwzd/18ptbiaII7KqalyYZ0QlRshNYi+YWKkgbikqKIjA7Pv08rlEWhAOBI/RFWHl6ptRh+wR36OzxpuMaSaIvd6uD1//qObav8d26BFuQXmJm8YAXZj3zOpq3HscWp9a+vUe+oAoAF373F6uMf0lD4DGnxcWGVpFRY5QoDzU0KP5/8mWAwukp5VByp11oUn+GuFmuxOYiQ0McmWV1eS3KBOWy+v8GAsigU5BeYWbk9AoQTYTzmlzLFWrKnag9JUUmkmFK0FkVzUjJjqTgSPqU83NViwVUIUCAwYw/bHBGtUIpC4XrYGvsBoIs6CoRXQlZhdSEjkkZoLUZQkJoZR31VM82N4XGWtGcuSF+Hazo7bpBhmyOiFUpRKCitsSCtyUinEX1UqVd7qGNz2Nhbs7fXu53cpGS6zqaoKAkPq8IzF6SfQ4dFSOqEDNscEa1QikLR+lDpcDYPQOehKMLhYdtXuw+7064silZSMuIAKD8cHvsU7hwRcFkUx/VOTMbwzBHREqUoFG0Pm6M5DX3kUcAZNglZQ+KH8N7M95iUNklrUYKC6D5GYhMjw2ZD250jkhFvItUhaIzWh22OiJaoqCdF20P17OrNNOvX0z+5kUd+dEFYPGwR+gjOSjlLazGCipTMuLCxKMD1/b1yzADMe6qJSYwkufXoV4Xv6BWKwmazUVJSQnNzs9aiBCVRUVHMHJVB7sC5XLfkXZ6+NoHLskNfSQC8s/sdsuOzOT/tfK1FCRpSB8ZxcHsF1mY7xqjwmAL0eh0Dz0rWWoywJTy+JaegpKSEuLg4srKyEEJVlfRESkllZSUlJSUMHTiUCF0Eu6p2cVn2ZVqL1mOklLyy9RWuGHyFUhQeHIqWfJcCLzy1lL5hcojR4Z2V6PSCjOFJWosSlvQKRdHc3KyURBcIIUhOTqa8vJwIfQTvznyXzLhMrcXqMfkF5tYTv37DZ4f0DI9QCVjgel+eXFnkyj0QhM0hRhuWHFCKwo/0CkUBKCVxEjzfm3AII/XM1gU9pdWExWToC9wJan3tApMUHIpwtuXMhPJ7c+UDeTQ3WLUWI2xRUU8KL47UH+GFTS9Q1limtSjdxj0ZRiSuxZj6JRBeCYQ9wZ0bc35zBBdbIjq0hyqRJgPxqdFaixG2KEURIPR6PXl5eW0/Bw8eZOPGjTzwwAOnfY+amhr+8pe/+FFKqLfW89aut9hXs8+v4/gT96Rn6LMNffTBDu29GXduzLcmGx/EtnRoD0UO76pkw+L92K0OrUUJW5SiCBAmk4ktW7a0/WRlZTFhwgRefPHFDn3t9s5r6QdCUeQm5vL9Td8zOX2yX8fxJ65Jz4E+qhRnc0a79t6NO2emWi9paH36Qz1nZl9BOdtWlqA3qOnMX/SaPQov3jiNMwmGzYDJD5zon3cTjL0ZGivhg9u8+97xebfEWLVqFc899xxLlizh6aefprS0lIMHD5KSksJjjz3GHXfcgdVqxel08vHHH/PEE0+wb98+8vLyuOSSS1i4cGG3xj0Zep0ePXqf3zeQzJuRy/wlXyN0NhwWl6II9cnQV7j3IRZ+VUj/Y1b0fYzcNDe0o56OH6wjdWAcQqf2If1F71QUGmCxWMjLywMgOzubTz75pEOfTZs2sWbNGkwmE/fffz+/+tWvuPnmm7FarTgcDhYsWMCOHTvYsmWLX2Vdfmg5HxR9wF8u/gt6XegojRORThbiUkuQgLM5g/SE8AgB9RXuQ4z++fg6UtPjuCyE3xe71UGVuZG8SwdqLUpY0zsVxZlaAJ79Y5K7ZUG4XU8nY/bs2ZhMLvfIpEmTePbZZykpKeHqq68mJyfnjMfsLqv3HmFd6Tpynn6LAdFZITHJekc6QYv+EBGOKJ6bczFXjwv9cF9/0C+rD0f31WotRo8oP9KA0ynpl9VHa1HCGuXUCyJiYmLa/n/TTTfx2WefYTKZmDFjBitWrAiIDPkFZj5Y6zLhdaYjIXM2hee5BAB60xEczRk8/3WxhlIFN32z+tBQ3UJjbcupOwcZ7lPt7v/zegAKGpo0lii8UYoiSNm/fz+DBw/mgQceYPbs2Wzbto24uDjq6/1bo2fh0kIsTUlIRyR6k+vIzFAILfWKaBJWdJFlOCyZKtLpJPTLjgfgzufWkv3I50xesCLoFwRwwno011jo79BRJ5w8vnR3SMgeqihFEaS8//77jBo1iry8PPbs2cNtt91GcnIykydPZtSoUcybN88v47omVh2O5kz0UUfatQcvnhFN+qhShHDisGSqSKeT8J+qOhxIIutsSAhJ6zHNrqPU4AyJxUwo0zv3KDSgoaHjQTHTpk1j2rRpADz99NNe1+bPn8/8+fM7vObf//63P8RrIy3BhLnGgsOSiTH5WxBWkMagn3Dnzcg9sUehs+Fo7ofRPoh5M1WkU1c8t7yY6XrJAPuJ9WIoZGm7Fy0xToiXOjbp7V7tCt+jLAqFF21nU1gyEcKJPsocEqGl7nMJ0hNMOBtzSKx+lN9fNTmoJzytKa2xUKp30t+hQ0jv9mDGvWiJcwrqheSoQXq1K3yPsigUXrgn1j98Y6UBSEw6yuNT5obEhOsO+3RKJzqh1kCnIi3BRKnVynirgb4OwbEQmXDd1mMZDv7Wx3V0QCgsZkIZ9TQpOjBnbDrrH55NZlwmU0Y1hoSScFPWWMaUd6ew/NByrUUJeubNyKUyClqQxDldkW6hMOF6Wo9CQHqiSZ1q52eURaHokksHXYrVGVoVOR3SwWXZlzGwj0rAOhVzxqYjpeT5pUWYa51Bn5jomVCZEW/itloj0+aOJPe8/lqLFvYoRaHokgfHP6i1CGdMemw6T056UmsxQoa54zKYOy7j1B01pn1CZWW1hd0tDuKP1ZGLUhT+RrmeFCdFSkmzPXSOkD1cdxindGotRkhhLqrmvf+3gfqq4P2c2ydUNukg32Tlz7tKNJSq96AURQB59tlnOeussxgzZgx5eXl8//33AR1/1apVzJo167T7SymZnT+bP/zwBz9K5TuabE3Mzp/NX7f+VWtRQorI6Aii+0RgtXRetTgYaB+JFensvF3hH5TrKUCsX7+eJUuWsHnzZiIjI6moqMBqDW7/vxCCa3KuISMu+F0TANsqtuGQDsakjNFalJAiJSOW2b8aq7UYJ8Wd3wOAhLvro9hutLN3QMTJX6jwCZooCiFEEvA+kAUcBK6TUlZ30s8BbG/99bCUcrYvxr/jqztO2efCjAu5fdTtbf2vGnoVc4bOobq5modWPeTV943L3jjl/Y4ePUpKSgqRkZEApKSkAK6KsQ899BANDQ2kpKTw5ptvMmDAAPbu3cvPf/5zysvL0ev1fPjhhwwePJiHH36YL7/8EiEEjz/+ONdffz2rVq3i6aefJiUlhR07djB+/Hj+9a9/IYTgq6++4sEHHyQlJYVx48ad4TtF23sQCmw+thmBIK9vntaihCSLNhzh+RXFlNZYSAuyjW3PhMpkp+sY1zqjCPoIrXBBK9fTI8ByKWUOsLz1986wSCnzWn98oiS04tJLL+XIkSMMGzaMe++9l2+//Rabzcb999/PRx99xKZNm7jzzjt57LHHALj55pu577772Lp1K+vWrWPAgAEsWrSILVu2sHXrVpYtW8a8efM4evQoAAUFBbzwwgvs2rWL/fv3s3btWpqbm7n77rtZvHgx3333HWVlZ368qZSSI3VHKG0o9en74Q82H9tMblIuccY4rUUJOd75907M/yiiqsoSlOU8PENiB7Zmkt88KydoFFm4o5Xr6SpgWuv/3wJWAb8N1OCnYwF01T8xKvGMXw8QGxvLpk2b+O6771i5ciXXX389jz/+ODt27OCSSy4BwOFwMGDAAOrr6zGbzcydOxeAqKgoANasWcONN96IXq+nX79+XHjhhfzwww/06dOHc889l4wMl4vIfdRqbGws2dnZbSXKb7nlFl599dUzktvmtDHn0zncMPwG5p3jn/pSvsDmsLG1fCvXDLtGa1FCkg+KjnEpggy7jmKjawMg2Mp5uBMql762g7L9tVwzNUtrkXoNWimKflLKowBSyqNCiL5d9IsSQmwE7MACKWV+Z52EEPcA9wAMHBi88fN6vb6tvtPo0aN5+eWXOeuss1i/fr1Xv7q6uk5fL6XstB1oc2m5x3EfpypEz079MuqNjEkdw8ZjG3t0H3+zs3InzY5mJvSboLUoIckOi4XpRJFp17cpCgi+zWIpJebiGjJyE3v83VacPn5zPQkhlgkhdnTyc9UZ3GaglHICcBPwghBiSGedpJSvSiknSCknpKam+kR+X1NYWEhx8YmzEbZs2cKIESMoLy9vUxQ2m42dO3fSp08fMjIyyM936cWWlhaampqYOnUq77//Pg6Hg/LyclavXs25557b5ZjDhw/nwIED7Nu3D4B33323W7JP6D+BPVV7qLf6t8R5T3ArsnH9znwfRgH9E02YDc42t46bYCvnUX20CUudlYzcRK1F6VX4TVFIKX8kpRzVyc+nwDEhxACA1n+Pd3GP0tZ/9+NyTwV3aMZJaGho4Cc/+QkjR45kzJgx7Nq1i2eeeYaPPvqI3/72t5x99tnk5eWxbt06AP75z3/y4osvMmbMGM4//3zKysqYO3cuY8aM4eyzz+aiiy7ij3/8I/37d51sFBUVxauvvsrMmTOZMmUKgwYN6pbs5/Q7B6d0svnY5m69PhBsOLqBoQlDSYpK0lqUkGTejFyOGiWpTh2mVoMiGMt5mItcMS/puQkaS9K7ECdzZ/htUCEWApVSygVCiEeAJCnlw+36JAJNUsoWIUQKsB64Skq562T3njBhgty40dtNsnv3bkaMGOHbPyLMONl71OJo4fx/n8+EpFns2H5h0EXF2Bw2Jr83mblD5zL/vI6l2RWnxwdf7aU8/zCfRbfQ0DcyaD5fT758ZTvHD9Vx27PnK9eTjxFCbGr14HRAq6inBcAlQohi4JLW3xFCTBBC/L21zwhgoxBiK7AS1x7FSZWEwj9E6iNJN41grfk/mGuCKyomv8DMhQu/pbL4Dj5dnaW5PKHMtZcMJiJKz/wJg1n7yEVBpySkU2IurCZjeJJSEgFGk81sKWUlcHEn7RuBn7b+fx0wOsCiKdrhLsRWru9HZN+tCH0j0uE621vrqBjv+j8DKWuG+YtcaTfBNsmFAjq9jvRhiZTsrtJalE6RwCV3nYUpViXZBRpVwkPRJZ5nE9sbhwKgj97n1UfLqBh3/Z+IpO/Qmw4AoXG+dzCTMTyR2nILdRXBFe0EoNMJBp2VTN9BfbQWpdehSngousSzEJuzOR3piEIfsxd7/YkSGVpGxZTWWEDYiExZhrV6Eg5L9ol2RbcYnJeKKS6CqCBZtXuWFp+iN3HltEFcd0mnwY8KP6IUhaJLvCdcPU2H7sFpPRF+rHVUjKv+DzQUPwHC5tWu6B5xSVHEJQVH2W5P16JewvhKydIv9mNMiVKuxQCjXE+KLmk/4Tpb0kC6VprpCdqfKuY+3xtpAKdLVq2VVzhQX9XM1uVHcDi0LdfuadE6BPy1TzPrI6zKtagBSlEEgMrKSvLy8sjLy6N///6kp6eTl5dHQkICI0eO7PQ1Tz75JMuWLTvlvQ8ePMioUaN8LTLgMRG34SCm3zfcNaMuKKJirspL46yxH5E6YAeC4FBe4cDxQ3Ws+bCYisMNmsrR3oXYonOdQ6Fci4FHuZ4CQHJyMlu2bAHg6aefJjY2lt/85jccPHiwy/MhnnnmmU7bHQ4Her2+02u+xj3hun3EaQmxRA3Yiyk2OMqOH6w7SGH99zw+4xKuHz5Ta3HChoFnJXPrf0+iT4q2Lry20uISZjZFUBjhYK/RqVyLGtArFcWhW287ZZ/YadNIvuvOtv7xc+eScPVc7NXVmB/4lVffQf98u9uyOBwO7r77btatW0d6ejqffvopJpOJ22+/nVmzZnHttdeSlZXFnXfeyddff80vf/lLcnJyuPPOO4mOjmbKlCndHvt0cBdic2NzXkCELjg2OteY1wAwJcO/70FvI8KoJ0JjJQEnSotHNzsZaTNQYnAq16JGKNeTxhQXF3Pfffexc+dOEhIS+PjjjzvtFxUVxZo1a7jhhhu44447ePHFFzsUEwwEbiWhRUa/m/wCM5MXrOB/Vi1CZ+vPD8Wnfo3izKgsbeDLV7ZrGibrLi0+1uCqntyYbFSuRY3olRbFmVoAnv0NiYk9siDak52dTV6e66Cd8ePHc/DgwU77XX/99QDU1tZSU1PDhRdeCMCtt97Kl19+6TN5TocHVz5IiimFxyc+HtBxwSMSxtFIbP/9WCovUEl2fkCv17G/oJz0YQmMmZ6pmRxzxqbj+KYMe6yDZY91XQBT4V+URaExXZUHb09MjCsbWkqpefkCg87AskPLcMrAR8W4I2EMsYUI4cTRMEIl2fmBhH7RJPaPZv+WCk3laKqzUnagluyzg7MqdG9BKYoQIyEhgfj4eNascfnn33nnnYDLMD1zOpXNlWwr3xbwsd0RL4bYXTjtMTgsA73aFb4hv8DMGksTRwqrmP7sCs1qaB3YWg4Sss9O0WR8hQulKEKQN954g/vuu49JkyZhMgV+03FqxlQMOgPLDy8P2JjufQkJIOwYYvdgbxiB+yusImF8h9u9t9nRjA5BdIVVswKQ+7eU0yclipSM2ICPrTiBJmXG/YkqM949zvQ9+vk3P2dXxT7shx7haE2zX8uOexf/A33sHqIz36Tp8O04GodjitCrTU4fMnnBiraw1HvqIqnQSxbFWklPMLH2kYsCJkdzo4035q3h7IszOf+aoQEbt7cSjGXGFSFOiphAtbWMsuZ9fi877pmhCyBtfbBWn4ejaahKsvMDbW48AUVGB1l2HZHOwLv3Dmwtx+mUDJ3Q1UnJikChFIWiWyzf1A8pdRjiTuxT+GtTuf0E5WxJo6VsLkIagiJDPNzwdOPtiXCgR5Bj0wfcvdcn2cSIyQNIHRgX0HEVHVGKQtEtyqp1OBpziIjfCpyIfvLHqtNzgtJFlqGLLAWk2pfwE56lW8r0kmqdk7PshoAnuqXnJnLRrSM0j/JTKEWh6CZpCSZstXnoImrQmw57tfsaz4nL3EtZ2QAAEAhJREFUmLwC08DXMUUIlaHrJ9yJbukJJoSAwkQdo8/tHzDLLb/AzJW/W8GYh79g8gLtIq4UJ+iVCXeKnjNvRi7zP6mn+agNR0s/wH+VW71qTh27ir5Jtcy/Ok+5nPxI+9ItgcIduHBtlYE8jPxTZ1EJlUGAUhSKbnFi8o6j1Gnxa9STezw1UWiHtdnOwe0V5Ezo51dXkDtw4bNoJ9GtAZlaH7mrUK6ngKHX69tKjefl5XVZquNMeeGFF2hqamr7PTY2cPHmc8ams+rhC/j97fX84Vaj3x/k363/XUBzNxQn2LvpON+8vovyw/V+Hce9x1Wrlxw1yA7tCm1QFkWAMJlMbaXGfYXD4eCFF17glltuITo62qf3Pl30Qs9bO9/ivAHnMSXdVcXV8/hKX1kahVWFfFT0EUPi1TGYWjB0fF8S+8f4PQIps4+Js4/a2RBp55iHolCBC9rSKxXFJ89vPmWfrNEpjL10YFv/4ZMGMOL8AVgarHz1yg6vvnP/a1y35GhubuYXv/gFGzduxGAw8Kc//Ynp06fz5ptvsnHjRl566SUAZs2axW9+8xumTZtGbGwsDz30EEuXLmXmzJmUlpYyffp0UlJSWLlyJQCPPfYYS5YswWQy8emnn9KvX79uyXc66ISOf8/8N4lRiUDH5Dh3fgX0zMf8QeEHROojuXLIlT0XWnHGGKMMDBgS77f7uxcXSeVWhtuMFEQ6wJWHr0qLBwHK9RQgLBZLm9tp7ty5ALz88ssAbN++nXfffZef/OQnNDc3n/Q+jY2NjBo1iu+//54nn3yStLQ0Vq5c2aYkGhsbmThxIlu3bmXq1Km89tpr/v3DoE1JWB3WDslx0PP8inprPYv3L2ZG1gziI/03WSm6Jr/AzJTfr+DuB77mzkd9G4nkXlyYqy2MazFQrnNi1rtCrlVCZXDQKy2KM7UAPPubYo3dsiA6cz2tWbOG+++/H4Dhw4czaNAgioqKTnofvV7PNddc0+V1o9HYdmre+PHj+eabb85Y1u7w2b7PeH7j85TW/RLo6AbriY95UfEiLHYLN4+4uQcSKrqLp5V4vtNIUrXksY99F4nkXlxk2nX0der4ymRFCgJeMkTRNcqi0JCu6mwZDAaczhNJbJ5WRlRU1EmPQo2IiGiLSjlZ2XJfk5uYS1VzFclpmzq93l0fs81h45+7/smEfhMYmdz5+eIK/+JpJW6ItBMnBdmN+CwL372IOK/FQKOQ7DY6vNoV2qMUhYZMnTq1rUx4UVERhw8fJjc3l6ysLLZs2YLT6eTIkSNs2LChy3vExcVRX+/fSJTTITcplynpU9AnrMFk9HY99cTHvGT/Eo41HePOUXf6QkxFN/CcsA8anBzTOzmvxcDRaktbVd/sRz7vdnJcWoKJ/nZBtl3Pxkg7dnGiXREcKEWhIffeey8Oh4PRo0dz/fXX8+abbxIZGcnkyZPJzs5m9OjR/OY3v2HcuK5dXffccw+XX34506dPD6DkXcgy5h6aHLXMnHLAldVLz3zMNqeNV7e9ysjkkW0RVYrA4zVhC1gfaSPJqWMcRtfeQo2lR4Uh583I5QKrEYuQFES6LGC1gR1cqDLjCsB379HPvvkZuyp38cXVXxBn7Fko5eJ9i3l0zaO8fPHLTM2Y2mPZFN2jfSQbEm5riCRSwj/iWnC0y7873b0Fd6STrqKFGxoi2RDnYLXe6vfkTUXnqDLjioDxq3G/oqalhte29Tza6vLsy/nTtD9xQfoFPpBM0V08az8BCAHfRtlIcOoY39IxHuZ09hbaIp1qLJzTbKBOONkc6eB/r89TFYGDEKUoFD7B7aueufAAEU3n8vauf7K/Zv8p+3fl225xtGDQGbhk0CWqemgQMGdsOmsfuYj0BBMSOBThpNjgYFKzgTin9+dzOnsLnhvkn0db+TTGSr1dnX0erPTK8FiFb2nvmqguuZSYIdu5/5v53DVkIc9/vdcrSxs4aVLetvJtPLDiAa7JeIL3vhM+zfBW9AxPa2GFycYd9ZFk2XRsj3R9lqe7t1BaY8HkBKuAFh2U6WSH+yuCB6UoFD2mwwl0jliay2ZzuHkXj23fjMUaAZxQCFERui6T8uaMTSfOGEdfYy5/+boOS4vR67WgqohqSVqCyXVMKlCnl7zWp5mmVr9E+hko87R4ExeUuL4D78VaQUU6BTVKUSh6TGerQHtdHvV1ebhmAIl7JrDYHB2UxIn7NLJo82Ge//oA5prZHa6rKqLaM29Grpc12KRzWRFPTxzClKEppOcmdnhNZ7W/5l2Wyyvv7sBpl21KQkU6BS9KUSh6jOcq8wSup18Y6jCl/4uW41fgsGSd5C5O4jI+5Yl179FYcwNdbZ8p14S2eJ0N0jrx/+aSYbR8WcoXGyt402ihtPYkbsZqC89/sIP/um4UP7txFAuXFiKUazHoUYoiQOj1ekaPHt32e35+PhUVFbz99tu8+OKLtLS0MHPmTCoqKpg/fz5Hjx7lnnvuaasKGxsbS0NDg1bin5T2q0xwrQ6jInTUWAGdFcmJDc8EUwQt/7+9e4+RqyzjOP79MV3YLRSh9OLCUneJhItNBCwFIdECTQoKVhEimCppjPwjBY2xQUOCJhJI3FCIQRNa1pKIICkQajVUhRISMKRICbS0RGwVBqhdyq3SQvfy+MeZXYZ15nS7OzNnLr9PstmZ2bMzz5vdnOec9/K8g8MfHX/IXjqOXUNMe5GBN88jbY6FuyayV2pvkAf2DvKrR7bx9r4h2iJJCGO7GdsCzt/Xxtz9OfrWvsTaGz27qVE4UdRIqVpP3d3dzJuXTFvetGkTAwMDo8d0d3dnWj78YJS6yiy+mty741pGTv5TZ23g66d/jk+293DXU1t5a3gzbdOfRLl9fLDzYgbeLr+wzl0T9evWJ7fz9tAQBCx+/1AOAZ4fGGJXbpDZIeYM5jjjwxzTQvztsEFe2Fub0jJWGS2ZKH7/s+sPeMwJZ8znzEsuHT3+M19cyNwFC9n73rv8YcXNHzv2GzfeMqE4Hn/8cXp7e+nr62PJkiX09/dz2mmnsXTp0szLhx+stB3oRhJI59HA7Ge4/5X1yQ9mwGHA4H8/zYe7LmL4w/JXlwczUGq1V9wl+M+2Ic76oI1L9n68Jlk+N8S6jgFemzI8uibDGkNLJoosjJQZB+jp6eGhhx4a/dmsWbNYtWoVvb29rFu3DoAVK1awYcMGZsyYAXxUPvymm25i+fLlrFy5khtuuKH2DTlIYxPI4PAituzeQn5PnvZcO99duZPhwaPK/n5HW85lphvA6DiVYNNhQzx36BCzh8RRw4cwTLAzF7yX8/4SjSqTRCHpcuCnwCnA/Ih4psxxFwK3AzlgVURM7NJ9jIO9Ayg+fuqRn5jQHcRkd7jLqnx4JZWa/dJ5hEoMhCd8F9E4xo5ThWDnlGAnyfORESr/TRtTViuzNwOXAk+UO0BSDrgDuAg4FbhSUsvWmc6qfHilFJdsKC4gd97JM+lo+3gXRUdbjttcyqGhjC3zMVbwUZL4xfqXJlVt1movk0QREVsj4kBr9ecDL0fE9ojYD9wHLK5+dPWhXsqHV0q5ne82bOsfPcFMttqsZWukzEe5gisjFweTrTZrtVfPYxTHAa8WPc8DZ5U6UNLVwNUAc+bMqX5kNTBSPryzs3N0MLuRlVv/8Po7+1IHwq3xlF5XAzkpdUW+1a+q3VFI+qukzSW+xntXUOrCpGRN9Ii4MyLmRcS8mTNnTjzoKiq1BmLBggWjg9fFjwGWLVvGtm3bRpNE8e9fdtllrF69uroBV1i59Q9eF9F8frTopJLdiUNltjTwIsr6V7VEERELI2Juia+Hx/kWeeD4ouddwOuVj9RqodzJw7Nfmk/xeEVxd2K58QtfLNS/eu562gicKKkHeA24AvhmtiHZRJVblOcuh+ZUrjux1Ap+XyzUv6ymx34N+CUwE/ijpOciYpGkY0mmwX4pIgYlXQOsJ5ke2xcRWyb6mRHhfQ3KqNUuhx6LaG2+WGhcLbEV6o4dO5g2bRrHHHOMk8UYEcHu3bvZs2cPPT09WYdjZhlJ2wq1nrueKqarq4t8Pk9/f3/WodSl9vZ2urq6sg7DzOpUSySKtrY2Xy2bmU2Q98w2M7NUThRmZpbKicLMzFI13awnSf3AvyfxFjOANysUTqNotTa3WnvBbW4Vk2nzpyKiZGmLpksUkyXpmXJTxJpVq7W51doLbnOrqFab3fVkZmapnCjMzCyVE8X/uzPrADLQam1utfaC29wqqtJmj1GYmVkq31GYmVkqJwozM0vlRFEg6UJJL0l6WdL1WcdTbZKOl7RB0lZJWyRdl3VMtSIpJ2mTpHUHPrrxSTpK0hpJ2wp/789nHVO1SfpB4f96s6R7JbVnHVOlSeqTtEvS5qLXpkv6i6R/FL4fXYnPcqIgOXEAdwAXAacCV0o6Nduoqm4Q+GFEnAKcDXyvBdo84jpga9ZB1NDtwCMRcTLwWZq87ZKOA64F5kXEXJL9bK7INqqqWA1cOOa164FHI+JE4NHC80lzokjMB16OiO0RsR+4Dxjv3t4NKSLeiIhnC4/3kJw8mn4HGUldwJeBVVnHUguSjgS+ANwFEBH7I+KdbKOqiSlAh6QpwFSacBvliHgCeGvMy4uBuwuP7wa+WonPcqJIHAe8WvQ8TwucNEdI6gZOB57ONpKauA1YDgxnHUiNnAD0A78pdLetknR41kFVU0S8BvQCrwBvAO9GxJ+zjapmZkfEG5BcDAKzKvGmThSJUtvetcS8YUlHAA8A34+I97KOp5okXQzsioi/Zx1LDU0BzgB+HRGnA+9Toe6IelXol18M9ADHAodLWpJtVI3NiSKRB44vet5FE96qjiWpjSRJ3BMRD2YdTw2cC3xF0r9IuhfPl/TbbEOqujyQj4iRu8U1JImjmS0EdkREf0QMAA8C52QcU638R1InQOH7rkq8qRNFYiNwoqQeSYeSDHytzTimqlKyefhdwNaIuDXreGohIn4cEV0R0U3yN34sIpr6SjMidgKvSjqp8NIFwIsZhlQLrwBnS5pa+D+/gCYfwC+yFriq8Pgq4OFKvGlLbIV6IBExKOkaYD3JDIm+iNiScVjVdi7wLeAFSc8VXvtJRPwpw5isOpYB9xQugrYDSzOOp6oi4mlJa4BnSWb3baIJy3lIuhdYAMyQlAduBG4B7pf0HZKEeXlFPsslPMzMLI27nszMLJUThZmZpXKiMDOzVE4UZmaWyonCzMxSOVGYmVkqJwozM0vlRGFWZZLOlPS8pHZJhxf2SZibdVxm4+UFd2Y1IOnnQDvQQVJ76eaMQzIbNycKsxoolM/YCHwAnBMRQxmHZDZu7noyq43pwBHANJI7C7OG4TsKsxqQtJaktHkP0BkR12Qcktm4uXqsWZVJ+jYwGBG/K+zP/pSk8yPisaxjMxsP31GYmVkqj1GYmVkqJwozM0vlRGFmZqmcKMzMLJUThZmZpXKiMDOzVE4UZmaW6n/Nz0zElY91PgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fifth segment\n",
    "xhat5 = np.linspace(my_pwlf_2.fit_breaks[4], my_pwlf_2.fit_breaks[5], 100)\n",
    "yhat5 = (my_pwlf_2.beta[0] +\n",
    "         (my_pwlf_2.beta[1])*(xhat5-my_pwlf_2.fit_breaks[0]) +\n",
    "         (my_pwlf_2.beta[2])*(xhat5-my_pwlf_2.fit_breaks[1]) +\n",
    "         (my_pwlf_2.beta[3])*(xhat5-my_pwlf_2.fit_breaks[2]) +\n",
    "         (my_pwlf_2.beta[4])*(xhat5-my_pwlf_2.fit_breaks[3]) +\n",
    "         (my_pwlf_2.beta[5])*(xhat5-my_pwlf_2.fit_breaks[4]) +\n",
    "         (my_pwlf_2.beta[6])*(xhat5-my_pwlf_2.fit_breaks[0])**2 +\n",
    "         (my_pwlf_2.beta[7])*(xhat5-my_pwlf_2.fit_breaks[1])**2 +\n",
    "         (my_pwlf_2.beta[8])*(xhat5-my_pwlf_2.fit_breaks[2])**2 +\n",
    "         (my_pwlf_2.beta[9])*(xhat5-my_pwlf_2.fit_breaks[3])**2 +\n",
    "         (my_pwlf_2.beta[10])*(xhat5-my_pwlf_2.fit_breaks[4])**2)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xhat, yhat, '-.', label='First')\n",
    "plt.plot(xhat2, yhat2, '-.', label='Second')\n",
    "plt.plot(xhat3, yhat3, '-.', label='Third')\n",
    "plt.plot(xhat4, yhat4, '-.', label='Fourth')\n",
    "plt.plot(xhat5, yhat5, '-.', label='Fifth')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Symbol\n",
    "from sympy.utilities import lambdify\n",
    "x = Symbol('x')\n",
    "\n",
    "def get_symbolic_eqn(pwlf_, segment_number):\n",
    "    if pwlf_.degree < 1:\n",
    "        raise ValueError('Degree must be at least 1')\n",
    "    if segment_number < 1 or segment_number > pwlf_.n_segments:\n",
    "        raise ValueError('segment_number not possible')\n",
    "    # assemble degree = 1 first\n",
    "    for line in range(segment_number):\n",
    "        if line == 0:\n",
    "            my_eqn = pwlf_.beta[0] + (pwlf_.beta[1])*(x-pwlf_.fit_breaks[0])\n",
    "        else:\n",
    "            my_eqn += (pwlf_.beta[line+1])*(x-pwlf_.fit_breaks[line])\n",
    "    # assemble all other degrees\n",
    "    if pwlf_.degree > 1:\n",
    "        for k in range(2, pwlf_.degree + 1):\n",
    "            for line in range(segment_number):\n",
    "                beta_index = pwlf_.n_segments*(k-1) + line + 1 \n",
    "                my_eqn += (pwlf_.beta[beta_index])*(x-pwlf_.fit_breaks[line])**k\n",
    "    return my_eqn.simplify()\n",
    "\n",
    "eqn1 = get_symbolic_eqn(my_pwlf_2, 1)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation number:  1\n",
      "-0.953964059782599*x**2 + 1.89945177490653*x + 0.00538634182565454\n",
      "Equation number:  2\n",
      "0.951561315686298*x**2 - 5.69747505830914*x + 7.5772216545711\n",
      "Equation number:  3\n",
      "-0.949735350431857*x**2 + 9.48218236957122*x - 22.720785454735\n",
      "Equation number:  4\n",
      "0.926850298824217*x**2 - 12.9824424358344*x + 44.5102742956827\n",
      "Equation number:  5\n",
      "-1.03016230425747*x**2 + 18.5306546317065*x - 82.3508513333073\n"
     ]
    }
   ],
   "source": [
    "eqn_list = []\n",
    "f_list = []\n",
    "for i in range(my_pwlf_2.n_segments):\n",
    "    eqn_list.append(get_symbolic_eqn(my_pwlf_2, i + 1))\n",
    "    print('Equation number: ', i + 1)\n",
    "    print(eqn_list[-1])\n",
    "    f_list.append(lambdify(x, eqn_list[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "yhat1 = f_list[0](xhat)\n",
    "yhat2 = f_list[1](xhat2)\n",
    "yhat3 = f_list[2](xhat3)\n",
    "yhat4 = f_list[3](xhat4)\n",
    "yhat5 = f_list[4](xhat5)\n",
    "xtemp = np.linspace(0,10, 1000)\n",
    "plt.plot(my_pwlf_2.x_data, my_pwlf_2.y_data, 'o')\n",
    "plt.plot(xtemp, my_pwlf_2.predict(xtemp), '-k', label='Predict')\n",
    "plt.plot(xhat, yhat1, '-.', label='First')\n",
    "plt.plot(xhat2, yhat2, '-.', label='Second')\n",
    "plt.plot(xhat3, yhat3, '-.', label='Third')\n",
    "plt.plot(xhat4, yhat4, '-.', label='Fourth')\n",
    "plt.plot(xhat5, yhat5, '-.', label='Fifth')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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